Akinori Nishino

The L(sl2) symmetry of the Bazhanov-Stroganov model associated with the superintegrable chiral Potts model

Abstract The loop algebra L ( sl 2 ) symmetry is found in a sector of the nilpotent Bazhanov–Stroganov model. The Drinfeld polynomial of a L ( sl 2 ) -degenerate eigenspace of the model is equivalent to the polynomial which characterizes a subspace with the Ising-like spectrum of the superintegrable chiral Potts model.

An Algebraic Derivation of the Eigenspaces Associated with an Ising-Like Spectrum of the Superintegrable Chiral Potts Model

AbstractIn terms of the

Chiral nonlinear Schrödinger equation

\mathfrak{sl}_{2}

Exact Scattering Eigenstates, Many-Body Bound States, and Nonequilibrium Current in an Open Quantum Dot System

loop algebra and the algebraic Bethe-ansatz method, we derive the invariant subspace associated with a given Ising-like spectrum consisting of 2r eigenvalues of the diagonal-to-diagonal transfer matrix of the superintegrable chiral Potts (SCP) model with arbitrary inhomogeneous parameters. We show that every regular Bethe eigenstate of the τ2-model leads to an Ising-like spectrum and is an eigenvector of the SCP transfer matrix which is given by the product of two diagonal-to-diagonal transfer matrices with a constraint on the spectral parameters. We also show in a sector that the τ2-model commutes with the

Fock Spaces for the Calogero Models with Distinguishable Particles

\mathfrak{sl}_{2}

Bosonic and fermionic eigenstates for generalized Sutherland models

loop algebra,

New nonsymmetric orthogonal basis for the Calogero model with distinguishable particles

L(\mathfrak{sl}_{2})

Rodrigues formulas for the non-symmetric multivariable polynomials associated with the BCN-type root system

, and every regular Bethe state of the τ2-model is of highest weight. Thus, from physical assumptions such as the completeness of the Bethe ansatz, it follows in the sector that every regular Bethe state of the τ2-model generates an

Rodrigues Formula for the Nonsymmetric Macdonald Polynomial

L(\mathfrak{sl}_{2})

Resonance in an open quantum dot system with a coulomb interaction : a bethe-ansatz approach

-degenerate eigenspace and it gives the invariant subspace, i.e. the direct sum of the eigenspaces associated with the Ising-like spectrum.